Ministers have launched a consultation on measures to protect victims of 'stranger stalking' amid fears the internet is fuelling an increase in cases.
The protection orders could help those targeted by stalkers outside of domestic settings and deter perpetrators before their fixations become "entrenched", the Home Office consultation says.
The legislation would also enable authorities to take steps to keep victims safe while gathering evidence for prosecution.
Officials said this should mean stalking is addressed earlier, giving protection to complainants ahead of cases reaching the courts.
The consultation document says stranger stalking, which could include a patient becoming fixated on their doctor or originate from online interaction on social media or chat rooms, may be increasing.
One reason for this could be that a growing usage of social networking and online communities may increase the opportunity for people to 'meet' and interact in some way," it says.
The internet can also "facilitate the ability for an individual to discover information about a person they are interested in", the document says.
This behaviour may become "extreme", it adds. In one case Elliot Fogel googled the name of victim Claire Waxman 40,000 times in a year.
More than 1,100 prosecutions were brought under the legislation in 2014/15, a rise of nearly 50% compared with the previous year.
The Suzy Lamplugh Trust, which manages the National Stalking Helpline, welcomed the consultation and said that more than half (55%) of those who contact the helpline are stalked by an acquaintance or stranger.